Version 1
: Received: 15 January 2018 / Approved: 22 January 2018 / Online: 22 January 2018 (04:22:52 CET)
How to cite:
Liu, W.; Yu, J.; Li, G. Global Existence, Exponential Decay and Blow-Up of Solutions for a Class of Fractional Pseudo-Parabolic Equations with Logarithmic Nonlinearity. Preprints2018, 2018010191. https://doi.org/10.20944/preprints201801.0191.v1
Liu, W.; Yu, J.; Li, G. Global Existence, Exponential Decay and Blow-Up of Solutions for a Class of Fractional Pseudo-Parabolic Equations with Logarithmic Nonlinearity. Preprints 2018, 2018010191. https://doi.org/10.20944/preprints201801.0191.v1
Liu, W.; Yu, J.; Li, G. Global Existence, Exponential Decay and Blow-Up of Solutions for a Class of Fractional Pseudo-Parabolic Equations with Logarithmic Nonlinearity. Preprints2018, 2018010191. https://doi.org/10.20944/preprints201801.0191.v1
APA Style
Liu, W., Yu, J., & Li, G. (2018). Global Existence, Exponential Decay and Blow-Up of Solutions for a Class of Fractional Pseudo-Parabolic Equations with Logarithmic Nonlinearity. Preprints. https://doi.org/10.20944/preprints201801.0191.v1
Chicago/Turabian Style
Liu, W., Jiangyong Yu and Gang Li. 2018 "Global Existence, Exponential Decay and Blow-Up of Solutions for a Class of Fractional Pseudo-Parabolic Equations with Logarithmic Nonlinearity" Preprints. https://doi.org/10.20944/preprints201801.0191.v1
Abstract
In this paper, we study the fractional pseudo-parabolic equations ut + (−△)su + (−△)sut = u log |u|. Firstly, we recall the relationship between the fractional Laplace operator (−△)s and the fractional Sobolev space Hs and discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence of global weak solution: for the low initial energy J(u0) < d, the solution is global in time with I(u0) > 0 or ∥u0∥X0(Ω) = 0 and blows up +∞ with I(u0) < 0; for the critical initial energy J(u0) = d, the solution is global in time with I(u0) ≥ 0 and blows up at +∞ with I(u0) < 0. The decay estimate of the energy functional for the global solution is also given.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
